We propose a novel approach to understanding conditional statements, viewing them as change descriptors within a standard nondeterministic framework. Our logical systems operate on a tree ordering, where the past is linear but the future is inherently uncertain and branching. We provide an axiomatization and demonstrate completeness for systems incorporating both a solely forward-looking conditional operator and a combination of backward and forward-looking operators. Additionally, we introduce and prove analogous results for the duals of these conditional operators, which naturally represent update operators by detailing the transformations leading to the current state.

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Conditional Logics of Nondeterministic Change

  • Konstantinos Georgatos

摘要

We propose a novel approach to understanding conditional statements, viewing them as change descriptors within a standard nondeterministic framework. Our logical systems operate on a tree ordering, where the past is linear but the future is inherently uncertain and branching. We provide an axiomatization and demonstrate completeness for systems incorporating both a solely forward-looking conditional operator and a combination of backward and forward-looking operators. Additionally, we introduce and prove analogous results for the duals of these conditional operators, which naturally represent update operators by detailing the transformations leading to the current state.